How could it be there are no modular forms of weight $2$ and level $4$. In the lmfdb database? We can easily think of one: $\theta(z)^4$ with $\theta(z)=\sum_{n\in \mathbb{Z}} q^{n^2}$ . Where are we supposed to look?
http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/4/2/1/?group=0
